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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 415 records · Page 23
All sourcesNASA NTRSDOE OSTI
DOE OSTI2026

Effects of Polymer Morphology on Solvent and Catalyst Accessibility during Polyethylene and Polystyrene Autoxidation

Efficient catalytic deconstruction of plastics requires facile solvent and catalyst access to polymer substrates to minimize mass transfer effects. Autoxidation using Co(II) acetate, Mn(II) acetate, and a radical carrier in acetic acid is a promising strategy to deconstruct mixed plastic waste, yet the role of polymer morphology in governing solvent and catalyst accessibility remains poorly understood. Here, in situ simultaneous small- and wide-angle X-ray scattering (SAXS/WAXS), complemented by X-ray fluorescence (XRF) imaging and high-pressure differential scanning calorimetry (DSC), were used to elucidate interactions between acetic acid, a Co/Mn catalyst solution, and semicrystalline polyethylene (PE) and amorphous polystyrene (PS) from room temperature to 160 °C. In PE, acetic acid and catalyst access were confined to amorphous regions and cryomilled particle interfaces at room temperature, while crystalline lamellae remained intact after soaking for up to 34 h. Increasing temperature enabled solvent uptake into PE, followed by solvent-assisted softening above 100 °C, and a modest melting-point depression that removed lamellar transport barriers upon melting. Conversely for PS, acetic acid penetrated the glassy polymer without inducing chain mobility until the glass transition was reached, above which the observed structural changes were consistent with enhanced segmental mobility which enabled bulk penetration. These results suggest that polymer morphology and thermally activated physical transitions arising from diffusion and polymer–solvent interactions can influence whether autoxidation of plastics is transport-limited or kinetically controlled, providing a framework for aligning reaction conditions with reaction outcomes.

09 BIOMASS FUELS↗
DOE OSTI2020

Timescales and Processes of Methane Hydrate Formation and Breakdown, With Application to Geologic Systems

Abstract Gas hydrate is an ice‐like form of water and low molecular weight gas stable at temperatures of roughly −10°C to 25°C and pressures of ~3 to 30 MPa in geologic systems. Natural gas hydrates sequester an estimated one sixth of Earth's methane and are found primarily in deepwater marine sediments on continental margins, but also in permafrost areas and under continental ice sheets. When gas hydrate is removed from its stability field, its breakdown has implications for the global carbon cycle, ocean chemistry, marine geohazards, and interactions between the geosphere and the ocean‐atmosphere system. Gas hydrate breakdown can also be artificially driven as a component of studies assessing the resource potential of these deposits. Furthermore, geologic processes and perturbations to the ocean‐atmosphere system (e.g., warming temperatures) can cause not only dissociation, but also more widespread dissolution of hydrate or even formation of new hydrate in reservoirs. Linkages between gas hydrate and disparate aspects of Earth's near‐surface physical, chemical, and biological systems render an assessment of the rates and processes affecting the persistence of gas hydrate an appropriate Centennial Grand Challenge. This paper reviews the thermodynamic controls on methane hydrate stability and then describes the relative importance of kinetic, mass transfer, and heat transfer processes in the formation and breakdown (dissociation and dissolution) of gas hydrate. Results from numerical modeling, laboratory, and some field studies are used to summarize the rates of hydrate formation and breakdown, followed by an extensive treatment of hydrate dynamics in marine and cryospheric gas hydrate systems.

58 GEOSCIENCES↗
DOE OSTI2020

A One‐Dimensional Model for Turbulent Mixing in the Benthic Biolayer of Stream and Coastal Sediments

Abstract In this paper, we develop and validate a rigorous modeling framework, based on Duhamel's Theorem, for the unsteady one‐dimensional vertical transport of a solute across a flat sediment‐water interface (SWI) and through the benthic biolayer of a turbulent stream. The modeling framework is novel in capturing the two‐way coupling between evolving solute concentrations above and below the SWI and in allowing for a depth‐varying diffusivity. Three diffusivity profiles within the sediment (constant, exponentially decaying, and a hybrid model) are evaluated against an extensive set of previously published laboratory measurements of turbulent mass transfer across the SWI. The exponential diffusivity profile best represents experimental observations and its reference diffusivity scales with the permeability Reynolds number, a dimensionless measure of turbulence at the SWI. The depth over which turbulence‐enhanced diffusivity decays is of the order of centimeters and comparable to the thickness of the benthic biolayer. Thus, turbulent mixing across the SWI may serve as a universal transport mechanism, supplying the nutrient and energy fluxes needed to sustain microbial growth, and nutrient processing, in the benthic biolayer of stream and coastal sediments.

Grant, Stanley B.↗
DOE OSTI2020

Nitrate Removal Across Ecogeomorphic Zones in Wax Lake Delta, Louisiana (USA)

Human activities have increased nitrate export from rivers, degrading coastal water quality. At deltaic river mouths, the flow of water through wetlands increases nitrate removal, and the spatial organization of removal rates influences coastal water quality. To understand the spatial distribution of nitrate removal in a river-dominated delta, in this study we deployed 23 benthic chambers across ecogeomorphic zones with varying elevation, vegetation, and sediment properties in Wax Lake Delta (Louisiana, USA) in June 2018. Regression analyses indicate that normalized difference vegetation index is a useful predictor of summertime nitrate removal. Mass transfer velocity were approximately three times greater on a vegetated submerged levee (13 mm hr –1 ), where normalized difference vegetation index was greatest, compared to other locations (4.6 mm hr –1 ). Two methods were developed to upscale nitrate removal across the delta. The flooded-delta method integrates spatially explicit potential removal rates across submerged portions of the delta and suggests that intermediate elevations on the delta—including submerged levees—are responsible for 70% of potential nitrate removal despite covering only 33% of the flooded area. The channel network method treats the delta as a network of river channels and suggests that although secondary channels are more efficient than primary channels at removing received nitrate, primary channels collectively contribute more to overall removal because they convey more of the total nitrate load. The two upscaling methods predict similar rates of nitrate removal, equivalent to less than 4% of nitrate entering the delta. To protect coastal waters against high nitrate loads, management policies should aim to reduce upstream nutrient loads.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2023

Multiscale Temporal Variability of the Global Air‐Sea CO 2 Flux Anomaly

Abstract The global air‐sea CO 2 flux (F) impacts and is impacted by a plethora of climate‐related processes operating at multiple time scales. In bulk mass transfer formulations, F is driven by physico‐ and bio‐chemical factors such as the air‐sea partial pressure difference (∆pCO 2 ), gas transfer velocity, sea surface temperature, and salinity–all varying at multiple time scales. To de‐convolve the impact of these factors on variability in F at different time scales, time‐resolved estimates of F were computed using a global data set assembled between 1988 and 2015. The F anomalies were defined as temporal deviations from the 28‐year time‐averaged value. Spectral analysis revealed four dominant timescales of variability in F–subseasonal, seasonal, interannual, and decadal with relative amplitude differences varying across regions. A second‐order Taylor series expansion was then conducted along these four timescales to separate drivers across differing regions. The analysis showed that on subseasonal timescales, wind speed variability explains some 66% of the global F anomaly and is the dominant driver. On seasonal, interannual, and decadal timescales, the ∆pCO 2 effect controlled by the ∆pCO 2 anomaly, explained much of the F anomaly. On decadal timescales, the F anomaly was almost entirely governed by the ∆pCO 2 effect with large contributions from high latitudes. The main drivers across timescales also dominate the regional F anomaly, particularly in the mid‐high latitude regions. Finally, the driver of the ∆pCO 2 effect was closely connected with the relative strength of atmospheric pCO 2 and the nonthermal component of oceanic pCO 2 anomaly associated with dissolved inorganic carbon and alkalinity.

Environmental Sciences & Ecology↗
DOE OSTI2026

Effects of Dissolution Regimes on Flow Channelization and Solute Transport in 3D Fracture Networks: Insights From Graph‐Based Reactive Transport Modeling

We investigate how mineral dissolution reshapes flow pathways and solute transport in three‐dimensional discrete fracture networks using a computationally efficient graph‐based reactive transport model. The DFNs are inspired by field‐site observations of fractured carbonate and represent realistic connectivity and structural heterogeneity. Flow is simulated with the Reynolds equation, and dissolution follows first‐order kinetics with diffusive limitations captured through an effective mass‐transfer coefficient. By systematically varying two key dimensionless parameters, the effective Damköhler number (Da), governing reaction versus advection rates, and a transport parameter (Da), analogous to the Thiele modulus, distinct flow channelization regimes emerge: mildly channelized at low G, highly channelized at intermediate Da, and extreme wormhole formation at high Da and low G. Eulerian and Lagrangian analyses, including breakthrough curves, particle tortuosity, dispersivity, and flow channeling indicators quantitatively characterize the progression of dissolution‐driven network restructuring. Across all regimes, initial fracture heterogeneity persists. The results underscore how the interplay between this initial structure, advection, reaction, and diffusion critically shapes subsurface flow pathways, with implications for applications ranging from groundwater remediation to enhanced geothermal systems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2026

Hyporheic‐Zone Processes and Stream Oxygen Dynamics: Insights From a Multiscale Reactive Transport Model

Aquatic ecosystem metabolism encapsulates the daily fixation (gross primary production, GPP d ) and mineralization (ecosystem respiration, ER d ) of organic carbon. In fluvial systems, these are commonly estimated by inverse solutions to field observations using a model that describes oxygen concentrations varying in the water column in response to metabolic fluxes and air‐water gas exchange controlled by a rate coefficient (K 600 ). The most common conceptual model is the single‐station metabolism (SSM) model. The simplicity and flexibility of this conceptualization make it attractive; however, it implicitly assumes that all the processes that consume oxygen in fluvial systems can be lumped into a bulk estimate of respiration with poorly understood consequences for estimates of GPP d , ER d , and K 600 . Here, we focus on the implications of using SSM conceptualization when estimating metabolic fluxes from oxygen dynamics in channels where hyporheic exchange occurs. We use a new multiscale numerical model for reactive transport in streams that represents hyporheic exchange and streambed heterotrophic respiration. Nondimensionalization of this model reveals dimensionless groups that collectively control oxygen dynamics. Numerical experiments offer a mechanistic understanding of the impacts of hyporheic exchange on diel oxygen dynamics revealing that potential biases arise from neglecting mass transfer limitations. Specifically, we found that hyporheic exchange significantly affects diel oxygen dynamics, even for nonreactive streambed sediments. Moreover, while the SSM performs well in many situations, we find conditions where significant bias is produced by hyporheic exchange, even when oxygen data are well‐fitted. These situations pose a major challenge in the interpretation of metabolism assessment estimates.

Gomez‐Velez, Jesus D. [Oak Ridge National Laborato↗
DOE OSTI2022

Intra-crystalline mesoporous zeolite encapsulation-derived thermally robust metal nanocatalyst in deep oxidation of light alkanes

Zeolite-confined metal nanoparticles (NPs) have attracted much attention owing to their superior sintering resistance and broad applications for thermal and environmental catalytic reactions. However, the pore size of the conventional zeolites is usually below 2 nm, and reactants are easily blocked to access the active sites. Herein, a facile in situ mesoporogen-free strategy is developed to design and synthesize palladium (Pd) NPs enveloped in a single-crystalline zeolite (silicalite-1, S-1) with intra-mesopores (termed Pd@IM-S-1). Pd@IM-S-1 exhibited remarkable light alkanes deep oxidation performances, and it should be attributed to the confinement and guarding effect of the zeolite shell and the improvement in mass-transfer efficiency and active metal sites accessibility. The Pd–PdO interfaces as a new active site can provide active oxygen species to the first C–H cleavage of light alkanes. This work exemplifies a promising strategy to design other high-performance intra-crystalline mesoporous zeolite-confined metal/metal oxide catalysts for high-temperature industrial thermal catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Thermal stability and coalescence dynamics of exsolved metal nanoparticles at charged perovskite surfaces

Exsolution reactions enable the synthesis of oxide-supported metal nanoparticles, which are desirable as catalysts in green energy conversion technologies. It is crucial to precisely tailor the nanoparticle characteristics to optimize the catalysts’ functionality, and to maintain the catalytic performance under operation conditions. We use chemical (co)-doping to modify the defect chemistry of exsolution-active perovskite oxides and examine its influence on the mass transfer kinetics of Ni dopants towards the oxide surface and on the subsequent coalescence behavior of the exsolved nanoparticles during a continuous thermal reduction treatment. Nanoparticles that exsolve at the surface of the acceptor-type fast-oxygen-ion-conductor SrTi 0.95 Ni 0.05 O 3–δ (STNi) show a high surface mobility leading to a very low thermal stability compared to nanoparticles that exsolve at the surface of donor-type SrTi 0.9 Nb 0.05 Ni 0.05 O 3–δ (STNNi). Our analysis indicates that the low thermal stability of exsolved nanoparticles at the acceptor-doped perovskite surface is linked to a high oxygen vacancy concentration at the nanoparticle-oxide interface. For catalysts that require fast oxygen exchange kinetics, exsolution synthesis routes in dry hydrogen conditions may hence lead to accelerated degradation, while humid reaction conditions may mitigate this failure mechanism.

25 ENERGY STORAGE↗
DOE OSTI2025

Enhancing surface activity and durability in triple conducting electrode for protonic ceramic electrochemical cells

With the material system operating at lower temperatures, protonic ceramic electrochemical cells (PCECs) can offer high energy efficiency and reliable performance for both power generation and hydrogen production, making them a promising technology for reversible energy cycling. However, PCEC faces technical challenges, particularly regarding electrode activity and durability under high current density operations. To address these challenges, we introduce a nano-architecture oxygen electrode characterized by high porosity and triple conductivity, designed to enhance catalytic activity and interfacial stability through a self-assembly approach, while maintaining scalability. Electrochemical cells incorporating this advanced electrode demonstrate robust performance, achieving a peak power density of 1.50 W cm −2 at 600 °C in fuel cell mode and a current density of 5.04 A cm −2 at 1.60 V in electrolysis mode, with enhanced stability on transient operations and thermal cycles. The underlying mechanisms are closely related to the improved surface activity and mass transfer due to the dual features of the electrode structure. Additionally, the enhanced interfacial bonding between the oxygen electrode and electrolyte contributes to increased durability and thermomechanical integrity. This study underscores the critical importance of optimizing electrode microstructure to achieve a balance between surface activity and durability.

Protonic Ceramic Electrochemical Cells↗
DOE OSTI2023

Electromagnetic levitation containerless processing of metallic materials in microgravity: rapid solidification

Space levitation processing allows researchers to conduct benchmark tests in an effort to understand the physical phenomena involved in rapid solidification processing, including alloy thermodynamics, nucleation and growth, heat and mass transfer, solid/liquid interface dynamics, macro- and microstructural evolution, and defect formation. Supported by ground-based investigations, a major thrust is to develop and refine robust computational tools based on theoretical and applied approaches. This work is accomplished in conjunction with experiments designed for precise model validation with application to a broad range of industrial processes.

42 ENGINEERING↗
DOE OSTI2026

Accurate determination of chemical abundances near a supermassive black hole

The metal abundances in galactic nuclei carry key information on the history of star formation and mass transfer in central regions of galaxies. X-ray fluorescence analysis is a unique tool to reliably measure the abundances of various elements via simple physics. Here we present a new observation of the active nucleus in the Circinus galaxy with the XRISM satellite at unprecedented X-ray energy resolution. The fluorescent iron Kα line profile modified by Compton scattering indicates that the material responsible for its emission is cold and metal rich and is located ≳0.024 pc from the supermassive black hole, consistent with the dusty torus region. The abundance pattern derived from comparing fluorescent line intensities of different metals shows subsolar ratios of argon- and calcium-to-iron and a supersolar ratio of nickel-to-iron. This abundance pattern is best produced by a combination in number fraction of 92$^{+2}_{–4}$% core-collapse supernovae from progenitor stars less massive than 20$^{+3}_{–2}$ M ⊙ and 8$^{+4}_{–2}$% type Ia supernovae. This suggests that gas feeding the supermassive black hole was enriched by recent core-collapse supernovae. Our findings imply that in metal-rich environments stars more massive than about 20 M ⊙ directly collapse into black holes or make faint supernovae without ejecting heavy metals into the space.

Astronomy and AstroPhysics↗
DOE OSTI2025

Decoupling the catalytic and degradation mechanisms of cobalt active sites during acidic water oxidation

Advancement of iridium-free catalysts for the low-pH oxygen evolution reaction (OER) is required to enable multi-gigawatt-scale proton-exchange water electrolysis. Cobalt-based materials might address this requirement, but little is known about the mechanism of operation of these OER catalysts at low pH. Here we investigate the nature and evolution of the active cobalt sites along with charge- and mass-transfer processes that support their catalytic function within a cobalt–iron–lead oxide material using in situ spectroscopic, gravimetric and electrochemical techniques. We demonstrate that corrosion of the cobalt sites and their reformation through electrooxidation of dissolved Co 2+ do not affect the catalytic mechanism and are decoupled from the OER. The OER-coupled charge transfer is supported by Co (3+δ)+ -oxo-species, which are structurally different from those reported for alkaline/near-neutral conditions and are formed on a relatively slow timescale of minutes. These mechanistic insights might assist in developing genuinely practical catalysts for this vital technology.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Continuous liquid-phase synthesis of nickel phosphide nanoparticles in a helically coiled tube reactor

The continuous liquid phase synthesis of nickel phosphide (Ni 2 P) nanoparticles was studied in a helically coiled tube (HCT) reactor both in single-phase and two-phase slug flows. The reactants were nickel acetylacetonate and tri-n-octylphosphine (TOP) in a 1-octadecane solvent. For the single-phase mode, various parameters such as reaction temperature, residence time, TOP concentration, and P/Ni ratio were studied. It was found that lower temperatures of 320 and 340 °C resulted in the formation of mixed Ni 12 P 5 and Ni 2 P phases, while a higher temperature of 360 °C gave mostly Ni 2 P, with particle sizes increasing from 28 to 42 nm. Upon varying the contact time between 88 and 340 s at 360 °C, a likely sequence of reaction involved an amorphous phase that was transformed in parallel to Ni, Ni 12 P 5 , and Ni 2 P. When the flow in the HCT was changed to a two-phase slug flow by using N 2 to split the continuous liquid phase into small liquid columns, the product was nearly 100% Ni 2 P and the particle size was as small as 3–4 nm. This was attributed to the enhanced mass transfer in the small liquid columns of the slug flow that led to higher reaction rates. Finally, it is highlighted that the HCT operated in a slug flow is an efficient and continuous method for the fabrication of nanoparticles.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

The role of gas flow distributions on CO 2 mineralization within monolithic cemented composites: coupled CFD-factorial design approach

The carbonation kinetics of monolithic cementing composites are strongly affected by gas transport which is, in turn, influenced by microstructural resistances and the presence of liquid water within pore networks. The non-uniform gas flow distribution within the CO 2 mineralization reactor can impart mass transfer resistance in the monolith microstructure, which affects the uptake of CO 2 (“carbonation”) of the cementing composites. This paper demonstrates how the gas spatial distribution (velocity and flow rate; quantified by CFD analysis) and processing conditions (temperature, relative humidity, and flow rate; quantified by factorial design) affect drying and carbonation, and in turn, the engineering properties of a representative ‘monolithic’ carbonate-cemented concrete component (i.e., herein concrete masonry unit: CMUs, also known as concrete block). It is shown that the gas flow distribution affects drying front penetration and results in moisture and carbonation gradients within the monolith. Particularly, variations in drying kinetics caused by non-uniformity of the contacting gas velocity impose gradients in moisture saturation, which results in increasing microstructural resistance to CO 2 transport. The resultant non-uniform carbonate-mineral formation (i.e., carbonate cementation), if not controlled, can produce gradients in mechanical properties and may alter failure patterns upon loading. Finally, these insights inform the optimal design of gas flow distribution systems and processing conditions within CO 2 mineralization reactors for the manufacturing of low-CO 2 concrete components using CO 2 -dilute industrial flue gas streams.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2020

Engineering efficient bifunctional electrocatalysts for rechargeable zinc–air batteries by confining Fe–Co–Ni nanoalloys in nitrogen-doped carbon nanotube@nanosheet frameworks

Developing precious-metal-free bifunctional oxygen reduction and evolution reaction (ORR/OER) electrocatalysts is of great significance for several key energy conversion and storage systems, yet remains a formidable challenge. In this work, we systematically designed Fe–Co–Ni trimetallic nanoalloys encapsulated in nitrogen-doped carbon nanotube@nanosheet frameworks (FeCoNi-NC) for application as effective bifunctional ORR/OER electrocatalysts. The rational structural design of FeCoNi-NC provides hierarchical porosity coupled with greatly increased effective electrochemical specific area for exposing abundant active sites and enhanced mass-transfer capability toward the ORR/OER. Experimental observations and theoretical calculations confirmed that Fe–Co–Ni nanoalloys interacting with pyridinic nitrogen-rich carbon synergistically optimized the adsorption/desorption free energies of oxygen intermediates, thus significantly enhancing the intrinsic ORR/OER activity. Consequently, FeCoNi-NC exhibits remarkable bifunctionality for the ORR (half-wave potential of 0.89 V) and OER (1.54 V at 10 mA cm –2 ) with ΔE = 0.65 V, and even outperforms Pt/C–RuO 2 benchmarks. Moreover, the corresponding zinc–air battery shows large power density (315.2 mW cm –2 ), high capacity (803.78 mA h g –1 at 100 mA cm –2 ) and excellent cycling durability (over 100 hours at 50 mA cm –2 ), further testifying its practical applications. This work demonstrates an effective pathway to highly active non-precious-metal bifunctional catalysts toward sustainable energy technologies.

25 ENERGY STORAGE↗
DOE OSTI2021

Air separation via two-step solar thermochemical cycles based on SrFeO 3-δ and (Ba,La) 0.15 Sr 0.85 FeO 3-δ perovskite reduction/oxidation reactions to produce N 2 : rate limiting mechanism(s) determination

Two-step solar thermochemical cycles based on reversible reactions of SrFeO 3–δ and (Ba,La) 0.15 Sr 0.85 FeO 3–δ perovskites were considered for air separation. The cycle steps encompass (1) the thermal reduction of SrFeO 3–δ or (Ba,La) 0.15 Sr 0.85 FeO 3–δ perovskites driven by concentrated solar irradiation and (2) oxidation in air to remove O 2 and produce N 2 . Rate limiting mechanisms were examined for both reactions using a combination of isothermal and non-isothermal thermogravimetry for temperature-swings between 673 and 1373 K, heating rates of 10, 20, and 50 K min –1 , and O 2 pressure-swings between 20% O 2 /Ar and 100% Ar at atmospheric pressure. Evolved O 2 and associated lag due to transport behavior were measured with gas chromatography and used with measured sample temperatures to predict equilibrium compositions from a compound energy formalism thermodynamic model. Measured and predicted chemical equilibrium changes in deviation from stoichiometry were compared. Rapid chemical kinetics were observed as the samples equilibrated rapidly for all conditions, indicative that heat and mass transfer were the rate limiting mechanisms. Furthermore, the effects of bulk diffusion (or gas diffusion through the bed or pellet) were examined using pelletized and loose powdered samples and determined to have no discernable impact.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Nanoconfinement and mass transport in metal–organic frameworks

The ubiquity of metal–organic frameworks in recent scientific literature underscores their highly versatile nature. MOFs have been developed for use in a wide array of applications, including: sensors, catalysis, separations, drug delivery, and electrochemical processes. Often overlooked in the discussion of MOF-based materials is the mass transport of guest molecules within the pores and channels. Given the wide distribution of pore sizes, linker functionalization, and crystal sizes, molecular diffusion within MOFs can be highly dependent on the MOF-guest system. In this paper, we discuss the major factors that govern the mass transport of molecules through MOFs at both the intracrystalline and intercrystalline scale; provide an overview of the experimental and computational methods used to measure guest diffusivity within MOFs; and highlight the relevance of mass transfer in the applications of MOFs in electrochemical systems, separations, and heterogeneous catalysis.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗